使用Warshall算法构造传递闭包的C ++程序
如果给出了有向图，则确定给定图中所有顶点对(i,j)的顶点j是否可从另一个顶点i到达。可达到意味着从顶点i到j有一条路径。此可达性矩阵称为图的传递闭合。Warshall算法通常用于查找给定图G的传递闭包。这是一个实现该算法的C++程序。
算法
Begin
1.Take maximum number of nodes as input.
2.For Label the nodes as a, b, c …..
3.To check if there any edge present between the nodes make a for loop:
for i = 97 to less than 97 + number of nodes
for j = 97 to less than 97 + number of nodes
if edge is present do,
adj[i - 97][j - 97] = 1
else
adj[i - 97][j - 97] = 0
end loop
end loop.
4.To print the transitive closure of graph:
for i = 0 to number of nodes
c = 97 + i
end loop.
for i = 0 to number of nodes
c = 97 + i;
for j = 0 to n_nodes
print adj[I][j]
end loop
end loop
End范例程式码
#include<iostream>
using namespace std;
const int n_nodes = 20;
int main() {
int n_nodes, k, n;
char i, j, res, c;
int adj[10][10], path[10][10];
cout << "\n\tMaximum number of nodes in the graph :";
cin >>n;
n_nodes = n;
cout << "\nEnter 'y' for 'YES' and 'n' for 'NO' \n";
for (i = 97; i < 97 + n_nodes; i++)
for (j = 97; j < 97 + n_nodes; j++) {
cout << "\n\tIs there an edge from " << i << " to " << j << " ? ";
cin >>res;
if (res == 'y')
adj[i - 97][j - 97] = 1;
else
adj[i - 97][j - 97] = 0;
}
cout << "\nTransitive Closure of the Graph:\n";
cout << "\n\t\t\t ";
for (i = 0; i < n_nodes; i++) {
c = 97 + i;
cout << c << " ";
}
cout << "\n\n";
for (int i = 0; i < n_nodes; i++) {
c = 97 + i;
cout << "\t\t\t" << c << " ";
for (int j = 0; j < n_nodes; j++)
cout << adj[i][j] << " ";
cout << "\n";
}
return 0;
}输出结果
Maximum number of nodes in the graph :4 Enter 'y' for 'YES' and 'n' for 'NO' Is there an edge from a to a ? y Is there an edge from a to b ?y Is there an edge from a to c ? n Is there an edge from a to d ? n Is there an edge from b to a ? y Is there an edge from b to b ? n Is there an edge from b to c ? y Is there an edge from b to d ? n Is there an edge from c to a ? y Is there an edge from c to b ? n Is there an edge from c to c ? n Is there an edge from c to d ? n Is there an edge from d to a ? y Is there an edge from d to b ? n Is there an edge from d to c ? y Is there an edge from d to d ? n Transitive Closure of the Graph: a b c d a 1 1 0 0 b 1 0 1 0 c 1 0 0 0 d 1 0 1 0